Gear Research Articles

COMPOSITE SUBGRADE MODULUS FOR RIGID AIRFIELD PAVEMENT DESIGN BASED UPON MULTILAYER THEORY

This study, authored by Jacob Uzan and Matthew W. Witczak, presents a computational exploration of the composite subgrade modulus within rigid airfield pavement design, employing multilayer theory as utilized in the new USAGE pavement design method. The research focuses on comparing the effects of pavement geometry and loading configurations by equating base-subgrade systems with an equivalent composite subgrade system, based on producing equal maximum tensile stresses under similar conditions. The analysis reveals that the composite subgrade modulus is influenced by various factors including the properties of the base and subgrade, the thickness of the concrete layer, and the load configuration. A regression equation is developed to estimate the composite subgrade modulus of elasticity, considering factors such as pavement geometry and the number of gear wheels on the landing gear, which aligns well with existing FAA and PCA methodologies. This paper also includes a thorough review of current methods for determining the composite subgrade modulus, pointing out the limitations and variations between methods that utilize either field tests or computational approaches based on layered elastic theory. The implications of these variations on pavement life and performance are critically analyzed, emphasizing the importance of accurate modulus estimation in pavement design to accommodate various aircraft types and pavement conditions. In conclusion, the research validates the application of multilayer theory in estimating composite subgrade modulus, offering enhancements over traditional approaches by incorporating a wider range of design variables. This comprehensive analysis not only contributes to refining pavement design practices but also highlights the necessity for ongoing adjustments and validations within established methodologies. (Abstract generated by AI tool ChatGPT 4)

Comparative Efficiency and Performance Analysis of Spur Gear and Non-Circular (Square) Gear Hydraulic Pumps

Comparative Efficiency and Performance Analysis of Spur Gear and Non-Circular (Square) Gear Hydraulic Pumps

MATHEMATICAL MODEL AND OPTIMIZATION ALGORITHM ACCORDING TO THE CRITERIA OF MINIMUM CONTACT STRESS FOR INVOLUTE SPUR GEARS WITH INCREASED CONTACT RATIO

Reducing the mass and dimensions of involute spur gears is an actual task of modern mechanical engineering. One of the perspective ways to solve it is the use of gearing with an increased working tooth depth and profile contact ratio εα ≥ 2. The study is devoted to the development of optimal design methods for such gears. Optimality criteria is formulated as follows: the contact stresses in the pitch point must take a minimum value when all constructive, geometric, kinematic, and technological constraints are met, first, when the profile contact ratio εα ≥ 2 is ensured. Variables planning are defined. These are addendum coefficients of the basic racks tooth for pinion and wheel h*a1, h*a2; profile angle of the basic rack α; addendum modification coefficient of the pinion x1. Formed a system of constraints for the variables planning: the main functional constraint of the minimum value of the profile contact ratio: εα ≥ 2; constraint for the addendum coefficients of the basic racks tooth for pinion and wheel h*a1, h*a2; constraint for profile angle of the basic rack α; constraint for addendum modification coefficients x1, x2; absence of the cutter interference for tooth dedendum; absence of the sharpening for tooth addendum; absence of the mesh interference; ensuring the bending strength of pinion and wheel teeth. A method for solving the problem of optimal design is chosen. The method of probing the space of design parameters was chosen from all the variety. The points of the LPτ-sequence are used as test points. The method allows you to operate with a significant number of parameters – up to 51, provides a sufficiently large number of evenly distributed test points – up to 220. The algorithm for optimal design of gear has been developed. The main stages of the algorithm are as follows: setting input data (numerical constraints on design variables, gear parameters and its load); generation of LPτ-sequence for variables planning with simultaneous consideration of their numerical constraints; checking of functional constraints; additional verification calculations (if necessary) of the gearing contact strength; formation of an array of possible solutions; searching of the best solution variant (the test point corresponding to the minimum value of the objective function) by sorting the array.

DETERMINATION OF QUALITY AND LOAD INDICATORS OF GEAR WITH HCR ENGAGEMENT WHEN IT IS USED IN TRANSMISSION ELEMENTS OF EXISTING MACHINES

The article is devoted to the evaluation of the use of an involute spur gear with an increased overlap ratio (HCR engagement) in the wheel planetary gearbox of the T-150K tractor, which is similar to the on-board transmission of the T-150 crawler tractor. The main criterion for the design of new gears with HCR engagement is to obtain an overlap ratio greater than 2.03. Given that the task is to replace the existing gears of the planetary gearbox with new ones, such parameters as the center distance, the widths of the crowns of the gears and the number of satellites were unchanged. It was allowed to change the gear ratio of the new planetary gearbox within 3% compared to the basic one, but first of all, combinations of gear wheels of the planetary gear were considered, in which this parameter was as close as possible to the existing one. Transmissions with several standard modules were considered, which, on the one hand, allow to realize an overlap ratio of more than 2.03, and on the other hand, the bending stresses in the root of the tooth will not exceed the yield strength of the material. All calculations were carried out in the KISSsoft software package, which provides a comprehensive assessment of the quality and strength indicators of the planetary transmission, taking into account the simultaneous operation of all satellites and the elastic deformation of the teeth. In the qualitative indicators, the overlap ratio, specific slip and thickness of the tops of the teeth of all gears will be evaluated in order to prevent sharpening. Strength indicators will be presented by graphs of contact pressures in "solar gear-satellite" and "satellite-epicycle" pairs and bending stresses in all gears. All the results of the calculations were compared with those of the existing transmission in order to determine the feasibility of using the HCR clutch in the presented wheel gearbox.

MATHEMATICAL MODEL OF THE VOLUMETRIC STRESS-STRAIN STATE OF GEARS WITH ARBITRARY TOOTH SHAPE

This paper presents an effective method for numerical analysis of the bulk stress-strain state of a gear of a real configuration. Namely, the determination of the bending stress fields in the gear teeth fillets with regard to geometric parameters. The methods of the classical theory of elasticity in a three-dimensional formulation with mixed boundary conditions for a region with a complex boundary surface are used. The solution is given in displacements. The components of the elastic displacement vector at an arbitrary point in the domain are determined, followed by the components of the stress tensor at the same point using Cauchy's differential dependences and the generalized Hooke's law. One of the main difficulties in solving this problem was the problem of representing the entire elastic section of the wheel together with the teeth in the form of an implicit continuous function of a continuous argument, which decisively determines the possibility of applying the methods of elasticity theory and constructing boundary conditions. These difficulties were overcome by using the theory of R-functions to describe the boundary surface of the gear as a whole. The force transmitted by the tooth is introduced in the problem in such a way that the configuration and size of the modeled meshing field are taken into account with the possibility of varying the law of its distribution over the meshing field. Different positions of the instantaneous contact patch in terms of the meshing phase over the entire period of meshing of a pair of teeth are also taken into account. The numerical solution to the problem is based on the Ritz method, where a linearly independent orthonormalized system of Legendre polynomials is used to develop coordinate sequences, and the geometry of the region and boundary conditions are taken into account. The proposed mathematical model of the volumetric stress-strain state can be used both in scientific research and engineering practice at the stage of designing or finishing gears with arbitrary tooth shapes for any real gear meshing system, rational selection of the size and location of the meshing field, and modeling the shape of the instantaneous contact area by the meshing phase for the entire period of meshing of a pair of teeth.

CRITERIA AND OBJECTIVE FUNCTIONS IN THE RATIONAL DESIGN OF TWO-SHAFT GEARBOXES

The relevance of the scientific and practical task of forming criteria and objective functions in the rational design of two-shaft gearboxes is described. This has made it possible to understand the need to highlight the topic and conduct relevant research and scientific discussions on the issue. The most significant mass and dimensional characteristics of two-shaft gearboxes from the perspective of vehicle design have been identified and used as criteria for optimal and rational design. Specifically: the center distance, which determines the placement of the gearbox shafts and its height; the length of the gearbox, which determines one of the main overall dimensions of the gearbox; the weight of the gearbox, the reduction of which may be dictated by the requirements for the technical object and also leads to a reduction in the material used and energy consumption; and the probability of reliable operation. Objective functions corresponding to the criteria of optimal and rational design are formulated, which are expressed by functional dependencies between geometric-constructive parameters and mass-dimensional characteristics, and also take into account the strength aspects of the main elements of two-shaft gearboxes. The objective function of the minimum center distance allows reducing the sum of the center distances of all gear meshes of the gearbox, and considering the condition of equality of the center distances of the gearbox gear meshes among themselves, to preserve the structural features and arrangement of the gear meshes. The objective function of minimum length accurately characterizes the linear dimension (length) of the gearbox. It considers not only the widths of the gear teeth but also other indicators (clearances, bearings, synchronizers, etc.), which are significant additions and increase the accuracy of calculations. The objective function of minimum weight of the gearbox consists of the weights of its main elements, namely: gears, shafts, bearings, synchronizers, and housing with the shifting mechanism. These elements make the main contribution to the mass characteristic, and the weights of other parts will be neglected due to their small sizes and inclusion in the error, which may be permissible for estimation calculations. The objective function of maximum reliability probability is presented as a certain «integral» value, which contains all calculated coefficients of stress levels for bending and contact stresses. Also design variables are defined

A modern approach to the technological support of the manufacture of gear wheels and additive am-technologies

A modern approach to the technological support of the manufacture of gear wheels and additive am-technologies

Dynamic modeling and analysis of wind turbine gear-bearing coupling system considering tooth root crack and slicing coupling effect

Tooth root cracks would change the meshing stiffness excitation of the gears, increasing the vibration and noise of wind turbine gearbox. Currently, there is relatively little literature that focuses on the slicing coupling effect of cracked gears, leading to incomplete accuracy in solving the time-varying mesh stiffness (TVMS) of gears under cracked conditions, making it difficult to accurately reflect the impact of root crack excitations on the dynamic behavior of wind turbine gear-bearing coupled systems. In this work, The improved analytical calculation method is proposed for the TVMS and system vibration coupling solution of the cracked gear pair, considering the slicing coupling effect. The dynamic model of the wind turbine high-speed stage gear set is developed using the lumped parameter approach, and the rolling bearing is modeled using the Hertz contact theory. Then, the excitations of the gear-bearing coupling system are developed using an improved slicing method. Lastly, the dynamic model of the wind turbine gear-bearing coupling system that considers tooth root cracks and the slicing coupling effect is established and validated. The results indicate that The TVMS modification algorithm considering the slicing coupling effect can better depict the dynamic change of the gear meshing stiffness under the crack failure. Cracks could reduce the TVMS of the gear pair, neglecting the coupling effect between the sliced gear tooth gains the potential risks of overestimating the influence of the gear crack depth on the TVMS. In addition, Gear cracks excitation may alter the dynamic contact load amplitude of the bearing rolling elements, resulting in a tendency for the load-bearing area to decrease. Moreover, When the cracked teeth are involved in meshing, The decrease in mesh stiffness will result in a larger amplitude periodic shock response to the system vibration displacement and a sideband phenomenon near the mesh frequency, neglecting the coupling effect between the sliced gear tooth or simplifying the bearing to a linear support stiffness matrix gain the potential risks of underestimating the influence of the gear crack depth on the vibration displacement of the gear-bearing coupling system.

Experimental Study of the Kinematics of a Double-Row Planetary Mechanism Using Two Elliptical External Gears

Introduction. Mechanisms with non-circular gears are of wide interest to researchers and inventors due to their compactness and the implementation of a wide range of transfer functions. The development of this area is stimulated by the advancements and reduction in cost of mechanical processing and additive manufacturing technologies, as well as the use of applied mathematical modeling packages for the analysis and synthesis of non-circular gears. Traditionally, noncircular gears are used to transmit rotational motion between parallel axes with a variable ratio of angular velocities. However, their use in planetary gear schemes provides implementing various types of output link motion. The analysis of the papers on the research area shows that gears with movable rotation axes have not been sufficiently studied from the point of view of kinematics and dynamics. Most research papers reveal the theory of such mechanisms without verifying the results obtained in practice. This work is aimed at the experimental verification of the kinematics of a planetary mechanism with two external engagements, which contains elliptical gears.Materials and Methods. The kinematic model of the mechanism under study is built on the basis of the velocity diagram of its links, which made it possible to obtain expressions for finding an analogue of the angular velocity and the position function of the output shaft. The experimental study of kinematics was performed on a laboratory stand containing a model of a planetary mechanism with a set of replaceable gear wheels, absolute encoders on the input and output shafts of the mechanism, a controller, and a PC for recording and processing the signal. The analysis of the obtained results was performed on a computer using statistical analysis methods.Results. As a result of kinematic analysis, position functions were constructed for three alternative planetary mechanisms, which had different geometric parameters of the gears and made it possible to implement various types of motion of the output shaft: swinging motion, discontinuous motion, and unilateral uneven rotation.Discussion and Conclusion. The analysis of the experimental results showed the adequacy of the constructed mathematical model of kinematics to real mechanisms. The confidence interval of measuring errors at a reliability level of 95% was 0.16±0.08° for the first version of the mechanism, 0.57±0.22° — for the second version, and 0.08±0.26° — for the third. The proposed planetary mechanism with elliptical gears for implementing various types of motion can be used in drives of process equipment in numerous industries: chemical and food (mixers), oil refining (pumping units for crude production), mechanical engineering (compressors, pumps, automated machines), and others. The conducted kinematic studies of the planetary mechanism and their experimental analysis are needed for further dynamic and force investigations, as well as for the design of drives based on the proposed transmission.

Effects of discrete fibre reinforcements on the wear resistance behaviour of polyamide-based spur gears

Abstract In many situations, the polymer gears are the perfect replacement for traditional metal gears. Compared to metal gears, the polymer gears will generate more heat at the gear tooth contact surface and more wear loss. Hence, this study aims to decrease the wear loss and increase the load-carrying capacity of the polymer gears. To achieve this, the reinforcement materials were added to the base polymer gear material. In this study, Nylon-66 was chosen as the polymer matrix material and an isolated glass fibre and steel grid were used as the reinforcement materials. Three different types of polymer spur gears such as Polyamide Gear (Nylon-66), Reinforced Polyamide Gear (Nylon-66+Glass Fibre), and Hybrid Glass Fiber Steel Grid Gear (Nylon-66+Glass Fibre+Steel Grid) named PG, RPG and HGFSGG were fabricated using injection moulding machine and each type of gears were compared for wear loss and specific wear rate under the similar testing conditions. The wear test was performed in the Forschungsstelle fur Zahnrader und Getriebebau (FZG) test rig at 1500 rpm with an applied load of 20 N for 12.5 hours continuously. From the test results, it was identified that HGFSGG polymer spur gears have exhibited a lower surface temperature and better wear properties compared to the other two types of spur gears. From the Scanning Electron Microscope (SEM) analysis, it was noticed that the PG spur gear exhibited deep and uniform wear at the gear tooth surface. In contrast, RPG spur gear exhibited glass fibre distortion and abrasive-type wear. The SEM micrograph of HGFSGG spur gear reveals the presence of very few surface flaws in the gear tooth surface.

Analysis of spur gears drilled with radial holes on teeth surface for effective weight reduction

Analysis of spur gears drilled with radial holes on teeth surface for effective weight reduction

Experimental Investigation of the Wear of Some Polymer Gear Wheels Produced by Three-Dimensional Printer on the Variation of Fill Percentage and Shell Thickness

FDM additive manufacturing method has recently been widely used because it is very attractive in terms of cost and material loss compared to traditional manufacturing methods such as molding and milling. In previous studies, many researches have been carried out on the engineering strength of plastic gears produced by conventional methods, but with the discovery of new plastic forms by material science and the practical application of new production methods, researchers continue the researches on additive manufacturing gears. So far, many studies have investigated the wear variation, rotational speed and torque variation with variations in gear wheels produced with three-dimensional printers. In this study, using the ability of FDM technology to produce in layers, gear wheels with several variations in outer shell thicknesses and internal filling ratios were produced. The wear behaviors of these gear wheels produced with different variations were investigated. On the other hand, PETG and ABS polymers were also produced under the same conditions in order to provide material diversity in addition to PLA polymer, which has been used so far in many studies due to its low melting temperature and good printability. Then wear behaviors were observed under the same conditions using the FZG (Forschungsstelle fur Zahnrader und Getriebebebau) test setup. Thanks to additive manufacturing technology, polymer gear types were produced with fill ratios of 100% and 50% and outer shell thicknesses of 0.4 mm and 0.8 mm. The test specimens were operated against the steel gear at a torque of 1.5 Nm and a rotational speed of 900 rpm and the mass losses as a result of wear were compared. Thus, a comparison was made about the strength of polymer types with the variation of outer shell thickness and filling percentage.

Dynamic Response of Electromechanical Coupled Motor Gear System with Gear Tooth Crack

The motor gear system (MGS) is recognized for its potential in enhancing transmission efficiency and optimizing space utilization. However, the system is subjected to challenges, notably the occurrence of abnormal vibrations. These issues stem from the dynamic interaction between the motor and gears, the presence of nonlinear factors in gear system, and the impact of gear faults, all of which contribute to complex vibration patterns. Traditional dynamic models have been found to be inadequate in effectively addressing the complexities associated with electromechanical coupling problems in MGS. To address these limitations, a comprehensive analysis approach is proposed in this paper, which is grounded in the development of an electromechanical coupling model. This method involves establishing a coupled dynamic model of the motor and gear system, integrating numerical simulations, and experimental validations to thoroughly analyze the vibration characteristics of the system. Through this multifaceted methodology, a detailed analysis of the system’s vibration characteristics is conducted. The results indicate that internal excitations from tooth root cracks not only directly affect dynamic characteristics of the gear transmission system (GTS) but also indirectly influence dynamic behavior of the motor, which offers valuable insights into modeling integrated MGS and provides significant solutions for fault diagnosis within these systems.

Dynamic Characteristics of Gear System Under Compound Fault of Tooth Root Crack and Bearing Outer Ring

Research on single faults like tooth root cracks and bearing outer ring failures is well-established. However, existing studies often replace the actual crack propagation path with a simplified linear crack model, neglecting the variation in stress intensity factors. They do not account for the coupling effect between gear teeth when calculating gear mesh stiffness. In practice, gearbox failures are predominantly compound failures involving both gears and bearings. This paper simulates the actual crack propagation path based on Workbench, introduces a dual-tooth meshing zone method to address the tooth-to-tooth coupling effect, and establishes a dynamic model of a system with compound faults of tooth root cracks and bearing outer ring defects. The dynamic response of the system under different levels of deterioration is then investigated. The findings indicate that the crack propagation path exhibits a concave shape, with the curvature of the path increasing as the crack deteriorates. The time-varying mesh stiffness calculated by considering tooth-to-tooth coupling effects aligns more closely with the finite element results. By analyzing the evolution patterns of the impact components and sidebands during the deterioration process, the dynamic evolution trends of the coupling phenomenon between tooth root cracks and bearing outer ring faults are clarified.

An Investigation of Dynamic Behavior of Electric Vehicle Gear Trains

Abstract The automotive industry has been experiencing a significant transition toward electrified powertrains in recent years. A torsional model of a common type of electric vehicle (EV) drivetrains is proposed to demonstrate certain dynamic behaviors that are unique to such high-speed applications. This two-stage helical gear drive train is supported by three shafts and connects the electric motor to the vehicle axle. The gear mesh interfaces are modeled by periodically time-varying stiffnesses subjected to backlash and displacement excitations to represent gear tooth errors and modifications. In addition to these internal excitations, torque fluctuations caused by electric motor are included as the external excitations. Two different operating conditions are studied here: (i) steady-state response as the vehicle is operated under steady torque conditions and (ii) transient response during EV system transitions between the drive and regenerative (regen) braking modes of operation. The torsional model predictions are verified through comparisons to simulations from a deformable-body contact model. Parameter sensitivity studies are performed to demonstrate nonlinear behavior of a helical gear train caused by external torque fluctuations as well as the interactions between external and internal excitations. Finally, drivetrain structural modes are shown to respond to drive-regen transitions resulting in certain transient (vibro-impact) behavior with elevated dynamic mesh forces.

Influence of cryogenically treated hob on surface characteristics of spur gear

ABSTRACT This work presents a comparative study of the surface characteristics of spur gears produced from cryotreated and untreated hobs at various cutting speeds and feed rates keeping constant depth of cut. Furthermore, a Taguchi Grey Relational Analysis was used to optimize the hobbing process and ANOVA was conducted to analyze the influence of studied parameters. The experimental run, for which the highest gray relational grade was obtained, was considered the optimal cutting condition. The results revealed that cryogenic treatment of the hob significantly decreased the spur gear’s flank surface roughness ( R a and R max ) and microgeometric deviations ( F a , F β , F p and F r ). The optimization results revealed that a cutting speed of 400 rpm and a feed of 8 mm/min with a cryo-treated hob produced the best surface characteristics (i.e. R a = 0.30 μ m , R max = 2.77 μ m , F a = 10.60 μ m , F β = 20.03 μ m , F p = 10.40 μ mand F r = 20.20 μ m ). This study can assist manufacturing industries in selecting suitable operating parameters for obtaining high-quality gears.

Three-dimensional colour reconstruction of aviation spiral bevel gear tooth surface through fusion of image and point cloud information

Three-dimensional colour reconstruction of aviation spiral bevel gear tooth surface through fusion of image and point cloud information

Using a flea’s hind limb teeth as a slant rack cutter profile to create a helical gear pair tooth surface modification

Using a flea’s hind limb teeth as a slant rack cutter profile to create a helical gear pair tooth surface modification

A gear tooth side clearance adjustment device and measurement method

Abstract The paper describes a gear tooth side clearance adjustment device structure principle, tooth side clearance adjustment and measurement calculation method, with simple operation, measurement accuracy is easy to ensure, adjustable range, can be adjusted continuously, and comparative test verification, proved the feasibility of the technology.

Working ability of gear transmissions with gear wheels made of aluminum and titanium alloys

Working ability of gear transmissions with gear wheels made of aluminum and titanium alloys